> Here is another test, on the same theme, for which I cannot also easily find a fraud:
>
> {tst(n,x)=kronecker(x^2-4,n)==-1&&
> gcd(x^2-1,n)==1&&
> Mod(Mod(1,n)*(L+x^2-1),(L^2-x*L+1)*(L^2+x*L+1))^(n)==-L^3+(x^2-2)*L+x^2-1;}
>

n=2953711;x=285843 is a near-counterexample that comes from me testing over the two quadratics that form the quartic. gcd(x,n)==95281 and gcd(x^2-2,n)==31,

Paul

paulunderwooduk

... n=1934765;x=1219266 has gcd(x-1,n)==265. So 2) might be 1 or a product of primes each congruent 5 (mod 6) , but as greater n get tested I guess this rule